论文标题
竞争与意见网络中的均衡着色和分叉
Balanced Colorings and Bifurcations in Rivalry and Opinion Networks
论文作者
论文摘要
网络的平衡着色对可靠的同步模式进行了分类 - 那些由所有可允许的ODE的流动不变的子空间定义的模式。在对称网络中，明显平衡的着色是轨道着色，其中颜色对应于对称组的子组的轨道。所有其他平衡的着色都被认为是异国情调的。我们分析了应用程序中遇到的两种紧密相关类型的网络类型的平衡着色：受过训练的威尔逊网络，这些网络发生在双目竞争的模型和意见网络中，这些网络发生在决策模型中。我们给出了两个适用于两种类型网络的异国色彩的例子，并证明了Wilson网络最多有两个学识渊博的模式没有异国情调的色彩。我们讨论了外来色素如何影响分支的分支的存在和稳定性，以实现相应模型ODE的分叉。
Balanced colorings of networks classify robust synchrony patterns -- those that are defined by subspaces that are flow-invariant for all admissible ODEs. In symmetric networks the obvious balanced colorings are orbit colorings, where colors correspond to orbits of a subgroup of the symmetry group. All other balanced colorings are said to be exotic. We analyze balanced colorings for two closely related types of network encountered in applications: trained Wilson networks, which occur in models of binocular rivalry, and opinion networks, which occur in models of decision making. We give two examples of exotic colorings which apply to both types of network, and prove that Wilson networks with at most two learned patterns have no exotic colorings. We discuss how exotic colorings affect the existence and stability of branches for bifurcations of the corresponding model ODEs.
